Mathematics: The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.5 minutes. a. Calculate the expected arrival time. (Round your answer to 2 decimal place.) b. What is the probability that an elevator arrives in less than 1.1 minutes

The arrival time of an elevator in a 12-story dormitory

tchase0616

21.01.2022

a) The expected arrival time is 2.25 minutes.

b) 25.88% probability that an elevator arrives in less than 1.1 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X < x) = \frac{x - a}{b-a}$

The expected value of the uniform distribution is given by:

$M = \frac{a+b}{2}$

The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.5 minutes.

This means that a = 0, b = 4.5

a. Calculate the expected arrival time. (Round your answer to 2 decimal place.)

$M = \frac{a+b}{2} = \frac{0 + 4.5}{2} = 2.25$

The expected arrival time is 2.25 minutes.

b. What is the probability that an elevator arrives in less than 1.1 minutes

$P(X < 1.1) = \frac{1.1 - 0}{4.25 - 0} = 0.2588$

25.88% probability that an elevator arrives in less than 1.1 minutes

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